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x2y + xy2 + x2z + xz2 + y2z + yz2 +3xyz
=(x2y+x2z)+(xy2+xz2)+(y2z+yz2)+3xyz
=x2(y+z)+x(y2+z2)+yz(y+z)+2xyz+xyz
=x2(y+z)+x(y2+z2+2yz)+yz(y+z+x)
=(y+z)x(x+y+z)+yz(y+x+z)
=(x+y+z)(xy+xz+yz)
x2y + xy2 + x2z + xz2 + y2z + yz2 + 3xyz
=(x2y + xy2 + xyz) + (x2z + xyz + xz2) + (xyz + y2z + yz2)
=xy(x + y + z) + xz(x + y + z) + yz(x + y +z)
=(x + y + z)(xy + xz + yz)
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x2 + xy + 5x + 5y = ( x2 + xy ) + ( 5x + 5y ) = x( x + y ) + 5( x + y ) = ( x + y )( x + 5 )
x2 - y2 + 3x - 3y = ( x2 - y2 ) + ( 3x - 3y ) = ( x - y )( x + y ) + 3( x - y ) = ( x - y )( x + y + 3 )
x² + xy + 5x + 5y
= (x²+ xy) + ( 5x+5y)
= x(x+y) + 5(x+y)
= (x+y)(x+5)
x² - y² + 3x - 3y
= (x² - y²) + ( 3x -3y)
= (x-y)(x+y) + 3(x-y)
= (x-y)(x+y+3)
chúc bạn học tốt ^^
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\(=\left(x+y\right)\left(x^2-xy+y^2\right)+2x\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+2x\right)\)
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\(x^2-\left(a+b\right)xy+aby^2=x^2-axy-bxy+aby^2\)
\(=\left(x^2-axy\right)-\left(bxy-aby^2\right)=x\left(x-ay\right)-by\left(x-ay\right)\)
\(=\left(x-ay\right)\left(x-by\right)\)
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x(y+z)^2 - y(z-x)^2 +z(x+y)^2 - x^3 + y^3 - z^3 - 4xyz
=xy^2+2xyz+xz^2-yz^2+2xyz-x^2y+x^2z+2xyz+zy^2-x^3+y^3-z^3-4xyz
=xy^2+xz^2-yz^2-x^2y+x^2z+y^2z-x^3+y^3-z^3+2xyz
=(xy^2+2xyz+xz^2)-x^3-(yz^2+2xyz+x^2y)+y^3+(x^2z+2xyz+y^2z)-z^3
=x[(y+z)^2-x^2)-y[(z+x)^2-y^2]+z[(x+y)^2-z^2]
=x(-x+y+z)(x+y+z)-y(x-y+z)(x+y+z)+z(x+y-z)(x+y+z)
=(x+y+z)[-x^2+xy+xz-xy+y^2-yz+xz+yz-z^2]
=(x+y+z)[-x(x-y-z)-y(x-y-z)+z(x-y-z)]
=(x+y+z)(x-y-z)(z-x-y)
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a) x^3 - x + y^3 - y
= x^3 + y^3 - x- y
= ( x+ y)( x^2 - xy +y^2 ) - ( x+ y)
= ( x+ y)( x^2 - xy + y^2 - 1 )
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`#3107.101107`
`x(y - 1) + 3(y - 1)`
`= (x + 3)(y - 1)`
x(y-1)+3(y-1)
=(y-1)(x+3)
Giải thích: đặt y-1 ra làm chung .... đa thức còn x+3
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